An analytical formulation that relates the modal expansion coefficients of a given wave front to its local transverse phase derivatives is proposed. The modal coefficients are calculated as a weighted integral over the wave-front slopes. The weighting functions for each mode are the components of a two-dimensional vector whose divergence equals the corresponding mode function. This approach is useful for analytical phase reconstruction from the input data provided by shearing interferometers or Hartmann–Shack wave-front sensors. Numerical results for a simulated experiment in terms of a set of Zernike polynomials are given.
© 1995 Optical Society of America
E. Acosta, S. Bará, M. A. Rama, and S. Ríos, "Determination of phase mode components in terms of local wave-front slopes: an analytical approach," Opt. Lett. 20, 1083-1085 (1995)